In this thesis, I will present the $\beta$-TeVO$_4$ compound and its structural and magnetic properties. It exhibits spin chain behavior with ferromagnetic exchange coupling between nearest neighbors and antiferromagnetic coupling between next nearest neighbors. Geometric frustration induces various arrangements of magnetic moments in different phases of this compound. They consist of a vector-chiral (VC) groundstate at magnetic fields under 5 T, a spin-density-wave (SDW) at higher fields and a spin stripe phase in between the VC and SDW. Therefore, we expect distinct NMR spectrum for each of the phases. Previous magnetic measurements have demonstrated the presence of unusual spin dynamics in the spin stripe phase The objective of this thesis is finding how the NMR spectrum and relaxation times change with temperature across different magnetic phase transitions and thereby characterize the spin dynamics of each phase.
I measured $^{17}$O spectrum in the temperature region between 2 and 50 K. At higher temperatures, we observe 20 spectral lines due to four different crystallographic sites of the O$^{2-}$ ions and the nuclear spin of $^{17}$O I = 5/2. With decreasing temperature, only 5 spectral lines remain, corresponding to the oxygen ion that is least coupled to the neighbouring ions. At the transition from the disordered paramagnetic phase to the spin-density-wave phase, the shape of the spectrum changes. Spectral lines split into U-shaped curves due to additional internal fields. At the transition into the stripe phase, spectral lines disappear. Relaxation-time measurements show a decrease of the spin-lattice and spin-spin relaxation times at the transition temperature from the spin-density-wave phase phase to the stripe phase, which is why the signal cannot be detected. Below the transition, the signal reappears with a different spectrum of more than 5 spectral lines, most likely corresponding to the remaining oxygen ions. Therefore, NMR measurements clearly show very distinct spin dynamics
in each of the magnetic phases of $\beta$-TeVO$_4$.
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